arXiv research

The dynamical analysis of American options has motivated the development of robust versions of the classical Snell envelopes. The cost of superhedging an American option is characterized by the upper Snell envelope. The infimum of the arbitrage free prices is characterized by the lower Snell envelope. In this paper we …

We make a systematic study of (quasi-)plurisubharmonic envelopes on compact Kähler manifolds, as well as on domains of $\mathbb{C}^n$, by using and extending an approximation process due to Berman [Ber13]. We show that the quasi-psh envelope of a viscosity super-solution is a pluripotential super-solution of a given co…

The paper introduces a method to learn and apply value envelopes for faster online reinforcement learning.

Improves regression efficiency by separating material and immaterial parts of responses.

Study cash-subadditive risk measures without quasi-convexity.

A nonparametric method for time series analysis extracts envelopes, detects peaks, and clusters data.

Gradient descent converges linearly in finite-width networks with positive NTK and compatible conditions.

The paper studies dynamic star-shaped risk measures and their representation.

Efficiently computes quasiconcave envelope with limited data.

The paper explores non-convex risk measures and their characterizations.

Correct method found for drawing precise envelope of straight lines.

Study three discrete envelope types of polygon bisection lines.

Paper solves four problems of pseudo-circle envelopes in Minkowski plane.

Describes envelopes of Thurston metric on Teichmüller space.

Study circle families' envelopes and related curves.

Solves four problems related to circle families in the plane.

New Lie group approach for envelope surface computation.

Solves four problems related to sphere families in 3D space.

This paper explores geometric insights into discrete R-congruences and their envelopes.

Operating envelope is an important concept in industrial operations. Accurate identification for operating envelope can be extremely beneficial to stakeholders as it provides a set of operational parameters that optimizes some key performance indicators (KPI) such as product quality, operational safety, equipment effic…

Study on Laplacian determinant in isosceles triangles, finding equilateral triangle minimizes determinant.

This work uses Lasry-Lions envelopes to solve nonconvex optimization problems.

New geometric mechanism solves four envelope problems.

New methods help escape strict saddle points in nonsmooth optimization.

We consider the homogeneous and the non-homogeneous convex relaxations for combinatorial penalty functions defined on support sets. Our study identifies key differences in the tightness of the resulting relaxations through the notion of the lower combinatorial envelope of a set-function along with new necessary conditi…

The paper proves boundedness of envelopes in complex manifolds.

We prove that the forgetful functor from groupoids to pregroupoids has a left adjoint, with the front adjunction injective. Thus we get an enveloping groupoid for any pregroupoid. We prove that the category of torsors is equivalent to that of pregroupoids. Hence we also get enveloping groupoids for torsors, and for pri…

We give a global description of envelopes of geodesic tangents of regular curves in (not necessarily convex) Riemannian surfaces. We prove that such an envelope is the union of the curve itself, its inflectional geodesics and its tangential caustics (formed by the conjugate points to those of the initial curve along th…

Optimal transport adapted for contaminated probabilities, showing equivalence under specific conditions.

By using the support function on the $xy$-plane, we show the necessary and sufficient conditions for the existence of envelopes of horizontal lines in the 3D-Heisenberg group. A method to construct horizontal envelopes from the given ones is also derived, and we classify the solutions satisfying the construction.

We view conformal surfaces in the 4--sphere as quaternionic holomorphic curves in quaternionic projective space. By constructing enveloping and osculating curves, we obtain new holomorphic curves in quaternionic projective space and thus new conformal surfaces. Applying these constructions to Willmore surfaces, we show…

Smooth convergence to an enveloping cylinder proved for mean curvature flow of complete graphical hypersurfaces.

We study the geometry of Outer Space $CV_n$ in regard of the asymmetric Lipschitz metric via envelopes, that is the set of all geodesics between two points. In the simplicial structure of $CV_n$ the envelopes are polytopes. We construct a piecewise unique geodesic between any two points in $CV_n$ by concatenating edges…

Defines a calculus for integrating Moreau envelopes in differentiable programming.

One typical assumption in inverse reinforcement learning (IRL) is that human experts act to optimize the expected utility of a stochastic cost with a fixed distribution. This assumption deviates from actual human behaviors under ambiguity. Risk-sensitive inverse reinforcement learning (RS-IRL) bridges such gap by assum…

We consider smooth 1-parameter families of plane curves tangent to a semicubic parabola, when the curvature radius of their curves at the tangency point vanishes at the cusp point. We find the $\A$-normal form of these families, their envelopes and local patterns near the cusp. We obtain a new codimension 2 singularity…

Given any smooth plane curve α(s)representing a mirror that reflects light the usual way and any radiant light source at a point in the plane, the reflected light will produce a caustic envelope. For such an envelope, we show that there is an associated curve \b{eta}(s) and a family of circles C(s) that roll on \b{eta}…

A spacetime can be embedded in an enveloping space with all its extensions.

Training certifiable neural networks enables one to obtain models with robustness guarantees against adversarial attacks. In this work, we introduce a framework to bound the adversary-free region in the neighborhood of the input data by a polyhedral envelope, which yields finer-grained certified robustness. We further …

The envelope of straight lines affine normal to a plane curve C is its affine evolute; the envelope of the affine lines tangent to C is the original curve, together with the entire affine tangent line at each inflexion of C. In this paper, we consider plane curves without inflexions. We use some techniques of singulari…

The paper extends a theorem to Lie-Rinehart algebras and provides new decompositions of universal enveloping algebras.

For a pair of points in a smooth closed convex planar curve $γ$, its mid-line is the line containing its mid-point and the intersection point of the corresponding pair of tangent lines. It is well known that the envelope of the mid-lines ($EML$) is formed by the union of three affine invariants sets: Affine Envelope Sy…

In this paper, we further study the forward-backward envelope first introduced in [28] and [30] for problems whose objective is the sum of a proper closed convex function and a twice continuously differentiable possibly nonconvex function with Lipschitz continuous gradient. We derive sufficient conditions on the origin…

Enhances LLM quantization with MDBF, improving perplexity and accuracy.

We shall use the classical Perron envelope method to show a general existence theorem to degenerate complex Monge-Ampère type equations on compact Kähler manifolds.

Paper presents a method for identifying isotope envelopes in MALDI-ToF data.

Study of complex Hessian equations using subharmonic functions and geodesics.

Designing deterministic denominators for SGLD stabilizes large drifts.